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Popular >

derivative of sqrt(x^2-2x+3)

Solution

\frac{d}{d x} (x^{2} - 2 x + 3)

Solution

\frac{x - 1}{x ^{2} - 2 x + 3}

Solution steps

\frac{d}{d x} (x^{2} - 2 x + 3)

Apply the chain rule:

\frac{1}{2 x ^{2} - 2 x + 3} \frac{d}{d x} (x^{2} - 2 x + 3)

= \frac{1}{2 x ^{2} - 2 x + 3} \frac{d}{d x} (x^{2} - 2 x + 3)

\frac{d}{d x} (x^{2} - 2 x + 3) = 2 x - 2

= \frac{1}{2 x ^{2} - 2 x + 3} (2 x - 2)

Simplify

\frac{1}{2 x ^{2} - 2 x + 3} (2 x - 2) : \frac{x - 1}{x ^{2} - 2 x + 3}

= \frac{x - 1}{x ^{2} - 2 x + 3}

Popular Examples

derivative of \sqrt[3]{(x^2-4^2})

limit as x approaches-1 of x/(5sin(x+1))

x \to - 1 lim (\frac{x}{5 sin ( x + 1 )})

implicit (dy)/(dx),x-y=xy implicit derivative

\frac{d y}{d x}, x - y = x y

integral of (x^2+2)/(sqrt(x))

\int \frac{x ^{2} + 2}{x} d x

limit as x approaches 2 of sqrt(x+5)

x \to 2 lim (x + 5)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2-2x+3) ?
The derivative of sqrt(x^2-2x+3) is (x-1)/(sqrt(x^2-2x+3))
What is the first derivative of sqrt(x^2-2x+3) ?
The first derivative of sqrt(x^2-2x+3) is (x-1)/(sqrt(x^2-2x+3))